Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you find the slope from a linear equation in the form y = mx + b?

Back

In the equation y = mx + b, the slope (m) is the coefficient of x. It indicates the steepness and direction of the line.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means that the line is horizontal, indicating that there is no change in y as x changes.

Front

What is the significance of the equation y = 1/3x?

Back

The equation y = 1/3x represents a linear relationship where the slope is 1/3 and the y-intercept is 0.

Front

How can you determine the rate of change from a word problem?

Back

To determine the rate of change, identify how much the dependent variable changes for a unit change in the independent variable, often expressed as 'per' (e.g., miles per gallon).